Impacts of Structural Properties of Myosin II Filaments on Force Generation
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eLife Assessment
The authors present a useful agent-based model to study the tensile force generated by myosin mini-filaments in actin systems (bundles and networks); by numerically solving a mechanical model of myosin-II filaments, the authors provide insights into how the geometry of the molecular components and their elastic responses determine the force production. This work is of interest to biophysicists (in particular theoreticians) investigating force generation of motor molecules from a biomechanical engineering and physics perspective. The authors convincingly show that cooperative effects between multiple myosin filaments can enhance the total force generated, but not the efficiency of force generation (force per myosin) if passive cross-linkers are present. This work would benefit from a more extensive discussion of the relevance of the results in view of the existing experimental literature.
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Abstract
Cells need intracellular forces for their physiological functions, such as migration, cytokinesis, and morphogenesis. The actin cytoskeleton generates a large fraction of the forces via interactions between cytoskeletal components, such as actin filament (F-actin), myosin, and actin cross-linking proteins (ACPs). Myosin II plays the most important role in cellular force generation. Myosin II molecules self-assemble into filaments with different structures depending on myosin II isoforms and other conditions such as pH and ionic concentration. It has remained elusive how force generation in actomyosin structures is affected by the architecture of myosin II filaments. In this study, we employed an agent-based model to investigate the effects of the structural properties of myosin II filaments on force generation in disorganized actomyosin structures. We demonstrated that the magnitude of forces and the efficiency of force generation can vary over a wide range depending on the number and spatial distribution of myosin II filaments. Further, we showed that the number of myosin heads and the length of a bare zone at the center of myosin II filaments without heads highly affect the force generation process in bundles and networks. Our study provides insights into understanding the roles of the structural properties of myosin II filaments in actomyosin contractility.
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eLife Assessment
The authors present a useful agent-based model to study the tensile force generated by myosin mini-filaments in actin systems (bundles and networks); by numerically solving a mechanical model of myosin-II filaments, the authors provide insights into how the geometry of the molecular components and their elastic responses determine the force production. This work is of interest to biophysicists (in particular theoreticians) investigating force generation of motor molecules from a biomechanical engineering and physics perspective. The authors convincingly show that cooperative effects between multiple myosin filaments can enhance the total force generated, but not the efficiency of force generation (force per myosin) if passive cross-linkers are present. This work would benefit from a more extensive discussion of the …
eLife Assessment
The authors present a useful agent-based model to study the tensile force generated by myosin mini-filaments in actin systems (bundles and networks); by numerically solving a mechanical model of myosin-II filaments, the authors provide insights into how the geometry of the molecular components and their elastic responses determine the force production. This work is of interest to biophysicists (in particular theoreticians) investigating force generation of motor molecules from a biomechanical engineering and physics perspective. The authors convincingly show that cooperative effects between multiple myosin filaments can enhance the total force generated, but not the efficiency of force generation (force per myosin) if passive cross-linkers are present. This work would benefit from a more extensive discussion of the relevance of the results in view of the existing experimental literature.
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Reviewer #1 (Public review):
Summary:
This work by Ding et al uses agent-based simulations to explore the role of the structure of molecular motor myosin filaments in force generation in cytoskeletal structures. The focus of the study is on disordered actin bundles which can occur in the cell cytoskeleton and have also been investigated with in vitro purified protein experiments.
Strengths:
The key finding is that cooperative effects between multiple myosin filaments can enhance both total force and the efficiency of force generation (force per myosin). These trends were possible to obtain only because the detailed structure of the motor filaments with multiple heads is represented in the model.
Weaknesses:
It is not clearly described what scientific/biological questions about cellular force production the work answers. There should be …
Reviewer #1 (Public review):
Summary:
This work by Ding et al uses agent-based simulations to explore the role of the structure of molecular motor myosin filaments in force generation in cytoskeletal structures. The focus of the study is on disordered actin bundles which can occur in the cell cytoskeleton and have also been investigated with in vitro purified protein experiments.
Strengths:
The key finding is that cooperative effects between multiple myosin filaments can enhance both total force and the efficiency of force generation (force per myosin). These trends were possible to obtain only because the detailed structure of the motor filaments with multiple heads is represented in the model.
Weaknesses:
It is not clearly described what scientific/biological questions about cellular force production the work answers. There should be more discussion of how their simulation results compare with existing experiments or can be tested in future experiments.
The model assumptions and scientific context need to be described better.
The network contractility seems to be a mere appendix to the bundle contractility which is presented in much more detail.
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Reviewer #2 (Public review):
Summary:
In this study, the authors use a mechanical model to investigate how the geometry and deformations of myosin II filaments influence their force generation. They introduce a force generation efficiency that is defined as the ratio of the total generated force and the maximal force that the motors can generate. By changing the architecture of the myosin II filaments, they study the force generation efficiency in different systems: two filaments, a disorganized bundle, and a 2D network. In the simple two-filament systems, they found that in the presence of actin cross-linking proteins motors cannot add up their force because of steric hindrances. In the disorganized bundle, the authors identified a critical overlap of motors for cooperative force generation. This overlap is also influenced by the …
Reviewer #2 (Public review):
Summary:
In this study, the authors use a mechanical model to investigate how the geometry and deformations of myosin II filaments influence their force generation. They introduce a force generation efficiency that is defined as the ratio of the total generated force and the maximal force that the motors can generate. By changing the architecture of the myosin II filaments, they study the force generation efficiency in different systems: two filaments, a disorganized bundle, and a 2D network. In the simple two-filament systems, they found that in the presence of actin cross-linking proteins motors cannot add up their force because of steric hindrances. In the disorganized bundle, the authors identified a critical overlap of motors for cooperative force generation. This overlap is also influenced by the arrangement of the motor on the filaments and influenced by the length of the bare zone between the motor heads.
Strengths:
The strength of the study is the identification of organizational principles in myosin II filaments that influence force generation. It provides a complementary mechanistic perspective on the operation of these motor filaments. The force generation efficiency and the cooperative overlap number are quantitative ways to characterize the force generation of molecular motors in clusters and between filaments. These quantities and their conceptual implications are most likely also applicable in other systems.
Weaknesses:
The detailed model that the authors present relies on over 20 numerical parameters that are listed in the supplement. Because of this vast amount of parameters, it is not clear how general the findings are. On the other hand, it was not obvious how specific the model is to myosin II, meaning how well it can describe experimental findings or make measurable predictions. The model seems to be quantitative, but the interpretation and connection to real experiments are rather qualitative in my point of view.
It was often difficult for me to follow what parameters were changed and what parameters were set to what numerical values when inspecting the curve shown in the figures. The manuscript could be more specific by explicitly giving numbers. For example, in the caption for Figure 6, instead of saying "is varied by changing the number of motor arms, the bare zone length, the spacing between motor arms", the authors could be more specific and give the ranges: ""is varied by changing the number of motor arms form ... to .., the bare zone length from .. to..., and the spacing between motor arms from .. to ..".
This unspecificity is also reflected in the text: "We ran simulations with a variation in either Lsp or Lbz" What is the range of this variation? "When LM was similar" similar to what? "despite different NM." What are the different values for NM? These are only a few examples that show that the text could be way more specific and quantitative instead of qualitative descriptions.
In the text, after equation (2) the authors discuss assumptions about the binding of the motor to the actin filament. I think these model-related assumptions and explanations should be discussed not in the results section but rather in the "model overview" section.
The lines with different colors in Figure 2A are not explained. What systems and parameters do they represent?
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Author response:
Public Reviews:
Reviewer #1 (Public review):
Summary:
This work by Ding et al uses agent-based simulations to explore the role of the structure of molecular motor myosin filaments in force generation in cytoskeletal structures. The focus of the study is on disordered actin bundles which can occur in the cell cytoskeleton and have also been investigated with in vitro purified protein experiments.
Strengths:
The key finding is that cooperative effects between multiple myosin filaments can enhance both total force and the efficiency of force generation (force per myosin). These trends were possible to obtain only because the detailed structure of the motor filaments with multiple heads is represented in the model.
We appreciate your comments about the strength of our study.
Weaknesses:
It is not clearly described what …
Author response:
Public Reviews:
Reviewer #1 (Public review):
Summary:
This work by Ding et al uses agent-based simulations to explore the role of the structure of molecular motor myosin filaments in force generation in cytoskeletal structures. The focus of the study is on disordered actin bundles which can occur in the cell cytoskeleton and have also been investigated with in vitro purified protein experiments.
Strengths:
The key finding is that cooperative effects between multiple myosin filaments can enhance both total force and the efficiency of force generation (force per myosin). These trends were possible to obtain only because the detailed structure of the motor filaments with multiple heads is represented in the model.
We appreciate your comments about the strength of our study.
Weaknesses:
It is not clearly described what scientific/biological questions about cellular force production the work answers. There should be more discussion of how their simulation results compare with existing experiments or can be tested in future experiments.
Thank you for the comment. First, our study explains why non-muscle myosin II in stress fibers shows focal distributions rather than uniform distributions; if they stay closely, they can generate much larger forces in the stress fibers via the cooperative overlap. Our study also predicts a difference between bipolar structures (found in skeletal muscle myosins and non-muscle myosins) and side polar structures (found in smooth muscle myosins) in terms of the likelihood of the cooperative overlap. As shown below, myosin filaments with the bipolar structure can add up their forces better than those with the side polar structure when their overlap level is the same. We will add discussion about these in the revised manuscript.
Author response image 1.
As the reviewer noticed, our results were briefly compared with prior observations in Ref. 4 (Thoresen et al., Biophys J, 2013) where different myosin isoforms were used for in vitro actin bundles. We will add more quantitative comparisons between the in vitro study and our results.
In addition, at the end of the conclusion section, we suggested future experiments that can be used for verifying our results. In particular, experiments with synthetic myosin filaments with tunable geometry seem to be suitable for verifying our computational predictions and observations.
The model assumptions and scientific context need to be described better.
We apologize for the insufficient descriptions about the model. We will revise those parts to better explain model assumptions and scientific context.
The network contractility seems to be a mere appendix to the bundle contractility which is presented in much more detail.
We included some cases run with the two-dimensional network in this study to prove the generality of our conclusions. We included minimal preliminary results in this study because we are currently working on a follow-up study with network structures. I hope that the reviewer would understand our intention and situation.
Reviewer #2 (Public review):
Summary:
In this study, the authors use a mechanical model to investigate how the geometry and deformations of myosin II filaments influence their force generation. They introduce a force generation efficiency that is defined as the ratio of the total generated force and the maximal force that the motors can generate. By changing the architecture of the myosin II filaments, they study the force generation efficiency in different systems: two filaments, a disorganized bundle, and a 2D network. In the simple two-filament systems, they found that in the presence of actin cross-linking proteins motors cannot add up their force because of steric hindrances. In the disorganized bundle, the authors identified a critical overlap of motors for cooperative force generation. This overlap is also influenced by the arrangement of the motor on the filaments and influenced by the length of the bare zone between the motor heads.
Strengths:
The strength of the study is the identification of organizational principles in myosin II filaments that influence force generation. It provides a complementary mechanistic perspective on the operation of these motor filaments. The force generation efficiency and the cooperative overlap number are quantitative ways to characterize the force generation of molecular motors in clusters and between filaments. These quantities and their conceptual implications are most likely also applicable in other systems.
Thank you for the comments about the strength of our study.
Weaknesses:
The detailed model that the authors present relies on over 20 numerical parameters that are listed in the supplement. Because of this vast amount of parameters, it is not clear how general the findings are. On the other hand, it was not obvious how specific the model is to myosin II, meaning how well it can describe experimental findings or make measurable predictions. The model seems to be quantitative, but the interpretation and connection to real experiments are rather qualitative in my point of view.
As the reviewer mentioned, all agent-based computational models for simulating the actin cytoskeleton are inevitably involved with such a large number of parameters. Some of the parameter values are not known well, so we have tuned our parameter values carefully by comparing our results with experimental observations in our previous studies since 2009.
We were aware of the importance of rigorous representation of unbinding and walking rates of myosin motors, so we implemented the parallel cluster model, which can predict those rates with consideration of the mechanochemical rates of myosin II, into our model. Thus, we are convincing that our motors represent myosin II.
In our manuscript, our results were compared with prior observations in Ref. 4 (Thoresen et al., Biophys J, 2013) several times. In particular, larger force generation with more myosin heads per thick filament was consistent between the experiment and our simulations.
Our study can make various predictions. First, our study explains why non-muscle myosin II in stress fibers shows focal distributions rather than uniform distributions; if they stay closely, they can generate much larger forces in the stress fibers via the cooperative overlap. Our study also predicts a difference between bipolar structures (found in skeletal muscle myosins and non-muscle myosins) and side polar structures (found in smooth muscle myosins) in terms of the likelihood of the cooperative overlap. As shown in Author response image 1, myosin filaments with the bipolar structure can add up their forces better than those with the side polar structure when their overlap level is the same. We will add discussion about these in the revised manuscript.
We will add more discussion about these in the revised manuscript.
It was often difficult for me to follow what parameters were changed and what parameters were set to what numerical values when inspecting the curve shown in the figures. The manuscript could be more specific by explicitly giving numbers. For example, in the caption for Figure 6, instead of saying "is varied by changing the number of motor arms, the bare zone length, the spacing between motor arms", the authors could be more specific and give the ranges: ""is varied by changing the number of motor arms form ... to .., the bare zone length from .. to..., and the spacing between motor arms from .. to ..".
This unspecificity is also reflected in the text: "We ran simulations with a variation in either Lsp or Lbz" What is the range of this variation? "When LM was similar" similar to what? "despite different NM." What are the different values for NM? These are only a few examples that show that the text could be way more specific and quantitative instead of qualitative descriptions.
We appreciate the comment. We will specify the range of the variation in each parameter in the revised manuscript.
In the text, after equation (2) the authors discuss assumptions about the binding of the motor to the actin filament. I think these model-related assumptions and explanations should be discussed not in the results section but rather in the "model overview" section.
Thank you for pointing this out. We will reorganize the text in the revised manuscript.
The lines with different colors in Figure 2A are not explained. What systems and parameters do they represent?
The different colors used in Fig. 2A were used for distinguishing 20 cases. We will add explanation about the colors in the figure caption in the revised manuscript.
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